Part IV - RIAA compensation
In the concept development phase we explained our reasons to go with passive RIAA compensation. We are talking about passive filter circuit with a carefully tailored output characteristic. There is almost an infinite number of R, L and C combinations that can give us the required response. Two most common (and simplest) configurations are shown below.
Even though both circuits will perform well, there are some minute differences. Circuit "A" will have capacitors C1 and C2 working in series at the high end of the frequency bandwidth. That means that their parasitic inductances and resistances will add up. Everything else being equal, circuit "B" does not have that drawback, having only C1 connected directly across the filter's output and C2 in series with R2, making C2 parasitics negligible in comparison the required high value for R2. So, we will go with circuit "B".
The filter circuit is really simple, indeed. Filter response is relatively easy to mathematically derive, however, equations in their closed form are pretty long (unlike those defining gain of the op-amp circuits). Luckily, should you decide to experiment with your own design, there are few good online calculators that work with pretty good.
Again, there is a large number of possible combinations (and online calculators make it easy to try many of them), but final choice will depend on circuits that are being connected at the input and output of the RIAA filter. Ideally, signals brough to the input should come from a source with a very low impedance. The filter's output should, ideally, be connected to an infinite impedance. Inevitable realities of practical circuits (non-zero input and non-infinity output impedance) will modify filter's response, it is our challenge to minimize the effects (or to qualify and compensate for them).
In our case, the filter will see very low impedance the op-amp output (few ohms) and filter output will be connected to the op-amp input (few hundred million, or even a billion ohms). Selecting R1 value to be about thousand times higher than op-amp's output impedance is a good compromise between filter accuracy and noise (high resistor values would help accuracy, but they will also have higher thermal noise, so it is on designer to pick his poison.... or how he mixes them).
Other than that, we need to be aware that calculations will give us results to few decimal points. Component vendors need to be more practical, though, so they make components with standardized values. We need to select and calculate values that are close to what is available on the market, or close to a combination of standard values (by adding components in series or parallel) and, if still not perfect, to understand and qualify effects.
Examining these effects, along with effects of component tolerances are the next steps we need to take.